Olaf played an important part in the conversion of the Norse to Christianity. He is said to have built the first church in Norway (in 995) and to have founded the city of Trondheim (in 997). A statue of Olaf Tryggvason is located in the city's central plaza.

Historical information about Olaf is sparse. He is mentioned in some contemporary English sources, and some skaldic poems. The oldest narrative source mentioning him briefly is Adam of Bremen's Gesta Hammaburgensis ecclesiae pontificum (c. 1070). In the 1190s, two sagas of Olaf Tryggvason were written in Iceland, by Oddr Snorrason and Gunnlaugr Leifsson. Snorri Sturluson gives an extensive account of Olaf in the Heimskringla saga, (c. 1230), using Oddr Snorrason's saga as his main source. The accuracy of these late sources is not taken at face value by modern historians and their validity is a topic of some debate. The following account is mainly based on the late saga sources.